Results 11 to 20 of about 70 (64)

Stability of a quartic functional equation. [PDF]

ScientificWorldJournal, 2014
We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x − my) = 2(7m − 9)(m − 1)f(x) + 2m2(m2 − 1)f(y)−(m − 1) 2f(2x) + m2{f(x + y) + f(x − y)} for a fixed positive integer m. We prove the Hyers‐Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach ...
Bodaghi A.
europepmc   +2 more sources

Approximate isomorphism of metric structures

Mathematical Logic Quarterly, Volume 69, Issue 4, Page 482-507, November 2023., 2023
Abstract We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and by Ben Yaacov, Doucha, Nies, and Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach‐Mazur ...
James E. Hanson
wiley   +1 more source

Unique Common Fixed Points for Occasionally Weakly Biased Maps of Type A in b‐Metric‐Like Spaces

Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023
We start this work by demonstrating the existence of unique common fixed points for two pairs of occasionally weakly biased maps of type A in a b‐metric‐like space, and we end it by producing two illustrative examples in order to support and show that our results are meaningful.
Hakima Bouhadjera, Hadeel Z. Alzumi, Wafa Shammakh, Saeed M. Ali, Mohammed S. Abdo, Salah Mahmoud Boulaaras   +5 more
wiley   +1 more source

Injective metrics on buildings and symmetric spaces

Bulletin of the London Mathematical Society, Volume 54, Issue 6, Page 2297-2313, December 2022., 2022
Abstract In this article, we show that the Goldman–Iwahori metric on the space of all norms on a fixed vector space satisfies the Helly property for balls. On the non‐Archimedean side, we deduce that most classical Bruhat–Tits buildings may be endowed with a natural piecewise ℓ∞$\ell ^\infty$ metric which is injective. We also prove that most classical
Thomas Haettel
wiley   +1 more source

Quartic Functional Equation: Ulam‐Type Stability in (β, p)‐Banach Space and Non‐Archimedean β‐Normed Space

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
In this study, we use the alternative fixed‐point approach and the direct method to examine the generalized Hyers–Ulam stability of the quartic functional equation g(u + mv) + g(u − mv) = 2(m − 1)(7m − 9)g(u) + 2(m2 − 1)m2g(v) − (m − 1)2g(2u) + m2{g(u + v) + g(u − v)}, with a fixed positive integer m/ge2 in the context of (β, p)‐Banach space.
Ravinder Kumar Sharma, Sumit Chandok, G Muhiuddin   +2 more
wiley   +1 more source

Penot’s Compactness Property in Ultrametric Spaces with an Application

Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021
In this work, we investigate the compactness property in the sense of Penot in ultrametric spaces. Then, we show that spherical completeness is exactly the Penot’s compactness property introduced for convexity structures. The spherical completeness property misled some mathematicians to it to hyperconvexity in metric spaces.
Mostafa Bachar, Messaoud Bounkhel, Samih Lazaiz, Shanhe Wu   +3 more
wiley   +1 more source

Tropical Lagrangian hypersurfaces are unobstructed

Journal of Topology, Volume 13, Issue 4, Page 1409-1454, December 2020., 2020
Abstract We produce for each tropical hypersurface V(ϕ)⊂Q=Rn a Lagrangian L(ϕ)⊂(C∗)n whose moment map projection is a tropical amoeba of V(ϕ). When these Lagrangians are admissible in the Fukaya–Seidel category, we show that they are unobstructed objects of the Fukaya category, and mirror to sheaves supported on complex hypersurfaces in a toric mirror.
Jeffrey Hicks
wiley   +1 more source

Haar null and Haar meager sets: a survey and new results

Bulletin of the London Mathematical Society, Volume 52, Issue 4, Page 561-619, August 2020., 2020
Abstract We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the techniques that may enable the reader to prove results in this area.
Márton Elekes, Donát Nagy
wiley   +1 more source

Boundary representations of locally compact hyperbolic groups

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract We develop the theory of Patterson–Sullivan measures for locally compact hyperbolic groups. This theory associates to certain left‐invariant metrics on the group measures on its boundary. Next, we establish irreducibility of the resulting (unitary) Koopman representations for second countable, nonelementary, unimodular locally compact ...
Michael Glasner
wiley   +1 more source

On generalizations of some fixed point theorems in semimetric spaces with triangle functions

Frontiers in Applied Mathematics and Statistics
In the present study, we prove generalizations of Banach, Kannan, Chatterjea, Ćirić-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mapping contracting perimeters of triangles.
Evgeniy Petrov, Ruslan Salimov, Ravindra K. Bisht   +2 more
doaj   +1 more source